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We are given a line $\overrightarrow r = \lambda(\hat i-\hat j+\hat k) $ which is the intersection of planes $ x+y=0$ and $y+z=0$.

How do I find the equation all planes passing through $ \overrightarrow r$ ?

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$\alpha(x+y)+\beta(y+z)=0$, $\alpha,\beta\in\mathbb{R}$, $\alpha^2+\beta^2\ne0$

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  • $\begingroup$ Can you please explain how do we get that? $\endgroup$ – Raghav May 1 at 16:07
  • $\begingroup$ Nevermind, got it. I think instead of $\alpha$ it will be just 1. Thanks. $\endgroup$ – Raghav May 1 at 16:10
  • $\begingroup$ $\alpha(x+y)+\beta(y+z)=0$ incldues all planes passing through $\vec{r}$ except $y+z=0$. $\endgroup$ – CY Aries May 1 at 16:14
  • $\begingroup$ Ohh, okay. Thanks $\endgroup$ – Raghav May 1 at 16:21
  • $\begingroup$ @amd Just amended my answer. Thanks. $\endgroup$ – CY Aries May 2 at 6:24

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